Derivative Problems, Please help

  • Thread starter dmitridj
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In summary, the conversation is about a problem involving a shrinking Tootsie Roll Pop and the question of how fast the radius will decrease when the pop is 20 mm across. The person is struggling with taking the derivative and asks for help. They are reminded to use the chain rule and to differentiate with respect to t.
  • #1
dmitridj
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Hey, I am having some trouble solving this problem..soon as i see how it works i just know i gunna go "Ooh, that's all i had to do" Here it is:

A shrinking lollipop. A shperical Tootsie Roll Pop that you are enjoying is giving up volume at a steady rate of 0.08 mL/min. How fast will the radius be decreasing when the Tootsie Roll Pop is 20 mm across?

Ok, I know I need to take the derivative of V=(4/3)pi(r^3) i just get lost in that process...please help..

THank you very much
 
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  • #2
They are asking you for [tex] \frac{dr}{dt} [/tex]

Why don't you differiantiate with respect to t?.
 
  • #3
dmitridj said:
Ok, I know I need to take the derivative of V=(4/3)pi(r^3) i just get lost in that process...please help..

Show me your derivative, so i can see where it went wrong.
 
  • #4
you need to use the chain rule, dV/dt = (dV/dr) (dr/dt)
 

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of one quantity with respect to another. In calculus, it is denoted as the slope of a tangent line to a curve at a specific point.

2. Why are derivatives important?

Derivatives are important because they allow us to find the rate of change of a function, which has many practical applications in science, engineering, and economics. They also help us to determine maximum and minimum values of a function, which is useful for optimization problems.

3. How do I find the derivative of a function?

The most common method for finding the derivative of a function is to use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules involve manipulating the algebraic form of the function to find the derivative.

4. What are some real-world applications of derivative problems?

Derivatives have many real-world applications, such as in physics to determine velocity and acceleration, in economics to analyze supply and demand curves, and in engineering to optimize designs and models.

5. Can I use technology to solve derivative problems?

Yes, there are many online calculators and software programs available that can solve derivative problems for you. However, it is important to understand the concepts and methods behind finding derivatives in order to properly interpret and apply the results.

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